Please help with these math problems.
[From: ] [author: ] [Date: 11-05-14] [Hit: ]
this is the solution.-1) 18, 20 2) let the speed of boat in east be x km/hrHence the speed of boat in north will be x+7 km/hrSince they travel with north and east direction, they form right angle triangleAfter 2 hours,(2x)^2 + (2(x+7))^2 = 26^26x^2 + 28x + 98 = 6763x^2 + 14x + 49 = 3383x^2 + 24x - 289 = 0Solving we get, x= 6.......
B - Consecutive even numbers will be close to the same value of each other (different only by 2). The square root of 360 is 18.973. Since you know that you must use two even numbers, and that it stands to reason that you'll need to use one number larger than the square-root of 360 and the other number smaller than the square-root of 360, your solution is to try 18 and 20. Sure enough, this is the solution.
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1) 18, 20
2) let the speed of boat in east be x km/hr
Hence the speed of boat in north will be x+7 km/hr
Since they travel with north and east direction, they form right angle triangle
After 2 hours,
(2x)^2 + (2(x+7))^2 = 26^2
6x^2 + 28x + 98 = 676
3x^2 + 14x + 49 = 338
3x^2 + 24x - 289 = 0
Solving we get, x= 6.5987, x = -14.599 (speed cant be negative)
Hence x= 6.6 km/hr (app)
East boat speed = x= 6.6 km/hr
North boat speed = x+17 = 13.6 km/hr
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1)
x
x+2
(x) * (x+2) =360
x^2 +2x = 360
x^2 + 2x - 360 = 0
x = {18, -20}
it could either be {18, 20} or {-20, -18} both should work
2)
x = rate of east bound boat
x+7 = rate of north bound boat
if one is traveling north and the other is east, they would actually form a right angle/right triangle
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i can add more work later but hopefully this gives you enough to work through the problem
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1 i think is 60. Or 40 and 90. Dont know about second 60 x60 =360 to figure simplify. 360 divded by 10 equals 36. Using simple multpy easy to figure out and understand. Best guess for second nb=20 eb=6. Dived 2 6 to get middle reach Point then add 7 to nb for his 7 hr advantage. Divide by 2 too each boat. Total is nb 10 km/h eb 3 km/h.
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For the first one, call your first integer m = k, then your next even integer n = k + 2, so n*m = 360. So n*m = k^2 + 2k = 360, so solve the quadratic k^2 + 2k - 360 = 0 to find your answer.
For the second one, say the first boat's speed is z, so ((z*2hrs)^2 + ((z + 7)*2hrs)^2)^(1/2) = 26 km
The formula I used was the Pythagorean equation for a right triangle, a^2 + b^2 = c^2 and z + 7 is the second boat's speed and z is the first boat's speed.
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